Estimation of multivariate binary density using orthogonal functions

In this paper, the authors studied certain properties of the estimate of Liang and Krishnaiah (1985, J. Multivariate Anal. 16, 162–172) for multivariate binary density. An alternative shrinkage estimate is also obtained. The above results are generalized to general orthonormal systems.     

On Bayes and unbiased estimators of loss

We consider estimation of loss for generalized Bayes or pseudo-Bayes estimators of a multivariate normal mean vector, θ. In 3 and higher dimensions, the MLEX is UMVUE and minimax but is inadmissible. It is dominated by the James-Stein estimator and by many others. Johnstone (1988, On inadmissibility of some unbiased estimates of loss,Statistical Decision Theory and Related Topics, IV (eds. S. S. Gupta and J. O. Berger), Vol. 1, 361–379, Springer, New York) considered the estimation of loss for the usual estimatorX and the James-Stein estimator. He found improvements over the Stein unbiased estimator of risk. In this paper, for a generalized Bayes point estimator of θ, we compare generalized Bayes estimators to unbiased estimators of loss. We find, somewhat surprisingly, that the unbiased estimator often dominates the corresponding generalized Bayes estimator of loss for priors which give minimax estimators in the original point estimation problem. In particular, we give a class of priors for which the generalized Bayes estimator of θ is admissible and minimax but for which the unbiased estimator of loss dominates the generalized Bayes estimator of loss. We also give a general inadmissibility result for a generalized Bayes estimator of loss. Research supported by NSF Grant DMS-97-04524.     

Analysis of blockwise shrinkage wavelet estimates via lower bounds for no-signal setting

A blockwise shrinkage is a popular procedure of adaptation that has allowed the statisticians to establish an impressive bouquet of asymptotic mathematical results and develop softwares for solving practical problems. Traditionally risks of the estimates are studied via upper bounds that imply sufficient conditions for a blockwise shrinkage procedure to be minimax. This article suggests to analyze the estimates via exact (non-asymptotic) lower bounds established for a no-signal setting. The approach complements the familiar minimax, Bayesian and numerical analysis, it allows to find necessary conditions for a procedure to attain desired rates, and it sheds a new light on popular choices of blocks and thresholds recommended in the literature. Mathematical results are complemented by a numerical study. Supported in part by NSF Grants DMS-9971051 and DMS-0243606.     

Estimation of Multinomial Probabilities under a Model Constraint

In this paper estimation of the probabilities of a multinomial distribution has been studied. The five estimators considered are: unrestricted estimator (UE), restricted estimator (RE) (under model ), preliminary test estimator (PTE) based on a test of the model , shrinkage estimator (SE) and the positive-rule shrinkage estimator (PRSE). Asymptotic distributions of these estimators are given under Pitman alternatives and the asymptotic risk under a quadratic loss has been evaluated. The relative performance of the five estimators is then studied with respect to their asymptotic distributional risks (ADR). It is seen that neither of the preliminary test and shrinkage estimators dominates the other, though each fares well relative to the other estimators. However, the positive rule estimator is recommended for use for dimension 3 or more while the PTE is recommended for dimension less than 3.     

Radiation formation of polymeric nanogels

An alternative method of synthesis of polymeric nanogels is proposed, based not on polymerization, but on intramolecular crosslinking of polymer chains, initiated by pulse irradiation in dilute aqueous solutions. Kinetic data show that for many water-soluble polymers irradiation under these conditions result in intramolecular crosslinking. Preliminary product studies on poly(vinyl alcohol) indicate that in fact internally crosslinked macromolecules can be obtained by this technique.     

The influence of Au-nanoparticles presence in PDMS on microstructures creation by ion beam lithography

3D microstructures in pure poly(dimethylsiloxane) (PDMS) and PDMS with embedded Au nanoparticles were prepared by ion beam lithography without any further etching. Two mega-electron volts helium and 10 MeV oxygen ions were used for ion microstructuring. Parallel lines of 1 mm in length and 10 μm in thickness were fabricated for investigation of the effect of the nanoparticles presence in the polymer on the surface morphology of the created microstructures. The created microstructures were checked by optical microscope. Infrared (IR) spectrometry was used to study the effect of the ions type and fluence on the chemical changes of the material. Atomic force microscopy was used for the fine detail study as well as for checking the microstructure quality. Analysis revealed an increased radiation resistance of the nanocomposite compared to the pure PDMS. Shrinkage is proportional to the fluence, but the maximum value for both materials is limited by saturation. 3D microstructure in modified PDMS obtained at the same irradiation condition as pure PDMS is characterized by its smaller height. Obtaining the microstructure in nanocomposite of the same height as in pure PDMS by increasing the fluence can be impossible due to saturation of shrinkage and/or radiation-induced heating of the material.     

水硬性石灰合成及拉破坏特性试验研究

水硬性石灰在欧洲石质文物修复和加固中获得了很大成功。我国的石质文物主要是砂岩,水硬性石灰的修复效果不好。为满足我国石质文物修复和加固的需求,本文以石灰石和黏土为原料,在950℃煅烧不同时间,制备出水硬性石,对试样的成分、微观形貌、收缩率、抗拉强度和拉破坏过程等进行了研究。结果表明:(1)试样中含有水硬性成分2CaO·SiO2(C2S);煅烧8h时,成分与欧洲水硬性石灰NHL5接近;1.5CaO·SiO2·xH2O(C-S-H)和CaCO3的含量随龄期的增加逐渐增加。(2)龄期1~3d,收缩率较小;龄期4~6d,收缩率以线性规律增加;7d以后,收缩率趋于稳定。(3)局部变形区随拉应力的增加而变大,邻近局部变形区逐渐合并,形成面积更大的应变局部化带;载荷超过峰值后,产生微裂隙;随载荷进一步增加,微裂隙扩展,贯穿整个试件,发展成宏观裂隙,使试件破坏。(4)抗拉强度随龄期的增加而增加,水硬性石灰中C-S-H、CaCO3等相互交织,构成空间致密体,使试件力学强度提高。合成的水硬性石灰物理力学性能与欧洲水硬性石灰NHL5相近,并且成分均匀、可控,在石质文物修复和加固工程中具有良好应用前景。     

聚乳酸/中药自然铜复合多孔膜的制备及其性能研究

采用冻干法制备了聚乳酸/中药自然铜复合多孔膜(PPCM),考察了中药自然铜对PPCM形态结构及力学性能的影响.实验结果表明自然铜的加入使PPCM的拉伸强度有轻微下降,但有利于其内孔的形成,并且可以有效地减小其在37℃恒温环境中的热收缩.成骨细胞体外培养实验证明中药自然铜具有促进成骨细胞在PPCM上生长和增殖的作用.     

Isometric crystallization of stretched poly(e-caprolactone) sheets for medical applications

Low melting temperature thermoplastic sheets based on poly(e-caprolactone) (PCL) can be formed directly on the patient and are used as immobilization device (mask) in the radiation therapy. The immobilization mask is allowed to harden in isometric conditions on the body at room temperature. A new method for isometric crystallization kinetics of thermoplastic polymer sheets is developed using a tensile-strength instrument. The isometric crystallization method allows investigating the shrinkage force on time of crystallization of stretched samples of thermoplastic polymer sheets or immobilization medical devices. The dependence of the shrinkage force on time is described by Avrami equation and the kinetics parameters of isometric crystallization are calculated. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effect of Injection Parameters and Addition of Nanoscale Materials on the Shrinkage of Polypropylene Copolymer

The effect of variation of injection conditions and addition of nano-calcium carbonate (CaCO₃), nano-silicon dioxide (SiO₂) and full-vulcanized nano-powdered styrene butadiene rubber (PSBR) on the shrinkage of injection-molded polypropylene-ethylene copolymer (90/10, co-PP) were investigated. The results showed that the shrinkage was different for different locations along the flow path. The shrinkage in the length direction of the injection-molded sample varied with the adjustment of the processing parameters, while the shrinkage in the width and thickness direction was almost unchanged. The addition of nano-CaCO₃ and PSBR decreased the shrinkage of co-PP, while the shrinkage of co-PP/ SiO₂ composite was almost unchanged.